Karim Shariff | NASA - National Aeronautics and Space Administration (original) (raw)

Papers by Karim Shariff

54th AIAA Aerospace Sciences Meeting, 2016

Annual Review of Fluid Mechanics, 2016

Turbulence modeling introduces one of the major sources of uncertainty in the prediction of aeron... more Turbulence modeling introduces one of the major sources of uncertainty in the prediction of aeronautical flows. This statement is even truer for supersonic flows for which physical insight is lacking and for which any modeling ideas that do exist remain unvalidated because of lack of data. Physical understanding and proper modeling of turbulent supersonic flow have seen a new beginning, however, thanks to a number of direct simulations by several groups in the last decade. For instance, an important effect which has recently come to light in free shear flows i s a significant reduction with Mach number in the ability of the flow to produce turbulent shear stress from turbulent energy.

Aps Division of Fluid Dynamics Meeting Abstracts, Nov 1, 1999

Radar has been proposed as one way to track wake vortices to reduce aircraft spacing. Radar echoe... more Radar has been proposed as one way to track wake vortices to reduce aircraft spacing. Radar echoes from aircraft wakes are usually interpreted qualitatively using Tatarski's theory of scattering by isotropic atmospheric turbulence. The present work predicts RCS by (1) Keeping the weak scattering approximation but dropping the assumptions of a far-field and a uniform incident wave, neither of which is generally valid for a coherent wake (2) Considering three simple mechanisms for the structure and magnitude of refractive index variations: (i) Radial density gradient in each vortex (ii) Adiabatic transport of atmospheric fluid in the oval surrounding the vortices (iii) 3D fluctuations in the vortex cores. For mechanism (ii) the predictions agree with available data. However, the predictions have a cut-off away from normal incidence which is not present in the measurements due possibly to 3D fluctuations in the oval. The reflectivity of mechanism (i) is comparable but cuts-off at frequencies lower than those considered in the experiment. Finally, we suggest that hot engine exhaust could increase RCS by 40 db and reveal vortex circulation, provided its mixing is prevented in the laminar vortices.

A number of advantages result from using B-splines as basis functions in a Galerkin method for so... more A number of advantages result from using B-splines as basis functions in a Galerkin method for solving partial differential equations. Among them are arbitrary order of accuracy and high resolution similar to that of compact schemes but without the aliasing error. This work develops another property, namely, the ability to treat semi-structured embedded or zonal meshes for two-dimensional geometries. This can drastically reduce the number of grid points in many applications. Both integer and non-integer refinement ratios are allowed. The report begins by developing an algorithm for choosing basis functions that yield the desired mesh resolution. These functions are suitable products of one-dimensional B-splines. Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented. The scheme is conservative and has uniformly high order of accuracy throughout the domain.

Aps Division of Fluid Dynamics Meeting Abstracts, Feb 1, 1996

The sound generated due to a localized flow over an infinite flat surface is considered. It is kn... more The sound generated due to a localized flow over an infinite flat surface is considered. It is known that the unsteady surface pressure, while appearing in a formal solution to the Lighthill equation, does not constitute a source of sound but rather represents the effect of image quadrupoles. The question of whether a similar surface shear stress term constitutes a true source of dipole sound is less settled. Some have boldly assumed it is a true source while others have argued that, like the surface pressure, it depends on the sound field (via an acoustic boundary layer) and is therefore not a true source. A numerical experiment based on the viscous, compressible Navier-Stokes equations was undertaken to investigate the issue. A small region of a wall was oscillated tangentially. The directly computed sound field was found to to agree with an acoustic analogy based calculation which regards the surface shear as an acoustically compact dipole source of sound.

We sketch a scenario for primary accretion of chondrite parent bodies based on turbulent concentr... more We sketch a scenario for primary accretion of chondrite parent bodies based on turbulent concentration of chondrule-size constituents into dense clumps, followed by slow gravitational contraction. We note key elements of the physics and describe the stati

Several mechanisms have been identified that create dense particle clumps in the solar nebula. Th... more Several mechanisms have been identified that create dense particle clumps in the solar nebula. The present work is concerned with the gravitational collapse of such clumps, idealized as being spherically symmetric. Calculations using the two-fluid model are performed (almost) up to the time when a central density singularity forms. The end result of the study is a parametrization for this time, in order that it may be compared with timescales for various disruptive effects to which clumps may be subject. An important effect is that as the clump compresses, it also compresses the gas due to drag. This increases gas pressure which retards particle collapse and leads to oscillation in the size and density of the clump. The ratio of gravitational force to gas pressure gives a two-phase Jeans parameter, JtJ_tJt, which is the classical Jeans parameter with the sound speed replaced by an the wave speed in a coupled two-fluid medium. Its use makes the results insensitive to the initial density ratio of particles to gas as a separate parameter. An ordinary differential equation model is developed which takes the form of two coupled non-linear oscillators and reproduces key features of the simulations. Finally, a parametric study of the time to collapse is performed and a formula (fit to the simulations) is developed. In the incompressible limit Jtto0J_t \to 0Jtto0, collapse time equals sedimentation time. As JtJ_tJt increases, the collapse time decreases roughly linearly with JtJ_tJt until Jtgtrsim0.4J_t \gtrsim 0.4Jtgtrsim0.4 when it becomes approximately equal to the dynamical time.

Aps Division of Fluid Dynamics Meeting Abstracts, 2003

The persistence of condensation trails, "contrails", in the far-field of an aircraft wake is nume... more The persistence of condensation trails, "contrails", in the far-field of an aircraft wake is numerically analyzed. Contrails are ice clouds formed by condensation of exhaust water vapor in a cold atmosphere. Their evolution and persistence are controlled by the wake dynamics, atmospheric turbulence, as well as by background water vapor content. Under suitable atmospheric conditions, they may trigger the formation of cirrus clouds, thus having a potential climate impact on regional/global scales. The object of the present study is to reproduce the contrail evolution numerically in intermediate scales (between aircraft- and atmosphere- scales) where exhaust mixing and clouds microphysics are expected to control their dynamics and, eventually, their transition to cirrus clouds. The simulations are carried out using a two-phase approach to deal with both gas and ice phases. Large eddy simulations are used for the gas phase while a Lagrangian particles tracking approach is used for ice crystals. Mass transfer between the two phases is used to account for vapor condensation, by employing available ice microphysics models. Besides the physical description of the phenomenon, the results may be useful for "calibrating" source terms, representative of the environmental impact of aircraft-generated emissions, in global climate codes.

Aps Division of Fluid Dynamics Meeting Abstracts, Feb 1, 1997

Initial results from the direct numerical simulation (DNS) of compressible turbulent boundary lay... more Initial results from the direct numerical simulation (DNS) of compressible turbulent boundary layers will be presented. The spatially developing boundary layer is first transformed to a parallel shear layer using a transformation similar to that used by Spalart for an incompressible boundary layer. This allows us to avoid inflow and outflow boundary conditions, and to apply periodic boundary conditions in the streamwise and spanwise directions. The resulting equations are then solved using a mixed Fourier B-spline Galerkin method. One challenge to these highly accurate and non-dissipative numerics has been the occurrence of sharp density gradients, which require significantly more resolution than the incompressible case, especially during transients. The first simulation is at Mach 2.5 with a momentum thickness Reynolds number based on wall viscosity of R_θ'=825. The simulations are used to examine the physics of the compressible boundary layer and to compute turbulence statistics and terms in the budget equations. The turbulence statistics include: rms and mean profiles, energy spectra, and two-point correlations.

When analytes containing cationic components, such as proteins, are separated in fused silica cap... more When analytes containing cationic components, such as proteins, are separated in fused silica capillaries or micro-chips, they adsorb strongly to the negatively charged walls. Broadened and highly asymmetric peaks in the detector signal is symptomatic of the presence of such wall interactions. Band broadening is caused by a reduction in wall zeta potential at the adsorbed sites which in turn introduces a shear into the electroosmotic flow which leads to Taylor dispersion. In this work, numerical solutions of the coupled electro-hydrodynamic equations for fluid flow and the transport equation for analyte concentration were undertaken in the limit of thin Debye layers. The calculations reproduce many of the qualitative effects of wall adsorption familiar from observation. Further, the simulation results are compared, and found to agree very well with a recently developed asymptotic theory (Ghosal, S., (2003) J. Fluid Mech., 491, 285--300.)

ABSTRACT Several two-equation turbulence models are compared to data from direct numerical simula... more ABSTRACT Several two-equation turbulence models are compared to data from direct numerical simulations (DNS) of the homogeneous elliptic streamline flow, which combines rotation and strain. The models considered include standard two-equation models and models with corrections for rotational effects. Most of the rotational corrections modify the dissipation rate equation to account for the reduced dissipation rate in rotating turbulent flows, however, the DNS data shows that the production term in the turbulent kinetic energy equation is not modeled correctly by these models. Nonlinear relations for the Reynolds stresses are considered as a means of modifying the production term. Implications for the modeling of turbulent vortices will be discussed.

Journal of Computational Physics, May 1, 1999

A numerical technique for computations of turbulent flows is described. The technique is based on... more A numerical technique for computations of turbulent flows is described. The technique is based on B-splines and allows grid embedding in physically significant flow regions. Numerical tests, which include solutions of nonlinear advection-diffusion equations and computations of flow over a circular cylinder at Reynolds numbers up to 300, indicate that the method is accurate and efficient. In computations of flow over a cylinder, the lift, drag, and base suction coefficients agree well with existing experimental data and previous numerical simulations.

Direct numerical simulations are performed for homogeneous turbulence with a mean flow having ell... more Direct numerical simulations are performed for homogeneous turbulence with a mean flow having elliptic streamlines. This flow combines the effects of rotation and strain on the turbulence. Qualitative comparisons are made with linear theory for cases with high Rossby number. The nonlinear transfer process is monitored using a generalized skewness. In general, rotation turns off the nonlinear cascade; however, for moderate ellipticities and rotation rates the nonlinear cascade is turned off and then reestablished. Turbulence statistics of interest in turbulence modeling are calculated, including full Reynolds stress budgets.

Aps Division of Fluid Dynamics Meeting Abstracts, Nov 1, 1997

The formation of vortex rings generated through impulsively started jets is studied through using... more The formation of vortex rings generated through impulsively started jets is studied through using a piston/cylinder arrangement. For a wide range of piston stroke to diameter ratios (L/D), the DPIV results indicate that the flow field generated by large L/D consists of a leading vortex ring followed by a trailing jet. The vorticity field of the formed leading vortex ring is disconnected from that of the trailing jet. On the other hand, flow fields generated by small stroke ratios show only a single vortex ring. The transition between these two distinct states is observed to occur at a stroke ratio of approximately 4, which, in this paper, is referred to as the "formation number". This number indicates the maximum circulation attainable by a vortex ring. The universality of this number was tested by generating vortex rings with different jet exit boundaries, as well as with various non- impulsive piston velocities. The mere existence of the "formation number" is intriguing since it hints at the possibility that nature uses this time scale for some evolutionary incentives such as optimum ejection of blood from the left atrium to the heart's left ventricle or locomotion process where ejection of vortices might have been utilized for the purposes of propulsion.

Aiaa Journal, Apr 30, 2012

54th AIAA Aerospace Sciences Meeting, 2016

Annual Review of Fluid Mechanics, 2016

Turbulence modeling introduces one of the major sources of uncertainty in the prediction of aeron... more Turbulence modeling introduces one of the major sources of uncertainty in the prediction of aeronautical flows. This statement is even truer for supersonic flows for which physical insight is lacking and for which any modeling ideas that do exist remain unvalidated because of lack of data. Physical understanding and proper modeling of turbulent supersonic flow have seen a new beginning, however, thanks to a number of direct simulations by several groups in the last decade. For instance, an important effect which has recently come to light in free shear flows i s a significant reduction with Mach number in the ability of the flow to produce turbulent shear stress from turbulent energy.

Aps Division of Fluid Dynamics Meeting Abstracts, Nov 1, 1999

Radar has been proposed as one way to track wake vortices to reduce aircraft spacing. Radar echoe... more Radar has been proposed as one way to track wake vortices to reduce aircraft spacing. Radar echoes from aircraft wakes are usually interpreted qualitatively using Tatarski's theory of scattering by isotropic atmospheric turbulence. The present work predicts RCS by (1) Keeping the weak scattering approximation but dropping the assumptions of a far-field and a uniform incident wave, neither of which is generally valid for a coherent wake (2) Considering three simple mechanisms for the structure and magnitude of refractive index variations: (i) Radial density gradient in each vortex (ii) Adiabatic transport of atmospheric fluid in the oval surrounding the vortices (iii) 3D fluctuations in the vortex cores. For mechanism (ii) the predictions agree with available data. However, the predictions have a cut-off away from normal incidence which is not present in the measurements due possibly to 3D fluctuations in the oval. The reflectivity of mechanism (i) is comparable but cuts-off at frequencies lower than those considered in the experiment. Finally, we suggest that hot engine exhaust could increase RCS by 40 db and reveal vortex circulation, provided its mixing is prevented in the laminar vortices.

A number of advantages result from using B-splines as basis functions in a Galerkin method for so... more A number of advantages result from using B-splines as basis functions in a Galerkin method for solving partial differential equations. Among them are arbitrary order of accuracy and high resolution similar to that of compact schemes but without the aliasing error. This work develops another property, namely, the ability to treat semi-structured embedded or zonal meshes for two-dimensional geometries. This can drastically reduce the number of grid points in many applications. Both integer and non-integer refinement ratios are allowed. The report begins by developing an algorithm for choosing basis functions that yield the desired mesh resolution. These functions are suitable products of one-dimensional B-splines. Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented. The scheme is conservative and has uniformly high order of accuracy throughout the domain.

Aps Division of Fluid Dynamics Meeting Abstracts, Feb 1, 1996

The sound generated due to a localized flow over an infinite flat surface is considered. It is kn... more The sound generated due to a localized flow over an infinite flat surface is considered. It is known that the unsteady surface pressure, while appearing in a formal solution to the Lighthill equation, does not constitute a source of sound but rather represents the effect of image quadrupoles. The question of whether a similar surface shear stress term constitutes a true source of dipole sound is less settled. Some have boldly assumed it is a true source while others have argued that, like the surface pressure, it depends on the sound field (via an acoustic boundary layer) and is therefore not a true source. A numerical experiment based on the viscous, compressible Navier-Stokes equations was undertaken to investigate the issue. A small region of a wall was oscillated tangentially. The directly computed sound field was found to to agree with an acoustic analogy based calculation which regards the surface shear as an acoustically compact dipole source of sound.

We sketch a scenario for primary accretion of chondrite parent bodies based on turbulent concentr... more We sketch a scenario for primary accretion of chondrite parent bodies based on turbulent concentration of chondrule-size constituents into dense clumps, followed by slow gravitational contraction. We note key elements of the physics and describe the stati

Several mechanisms have been identified that create dense particle clumps in the solar nebula. Th... more Several mechanisms have been identified that create dense particle clumps in the solar nebula. The present work is concerned with the gravitational collapse of such clumps, idealized as being spherically symmetric. Calculations using the two-fluid model are performed (almost) up to the time when a central density singularity forms. The end result of the study is a parametrization for this time, in order that it may be compared with timescales for various disruptive effects to which clumps may be subject. An important effect is that as the clump compresses, it also compresses the gas due to drag. This increases gas pressure which retards particle collapse and leads to oscillation in the size and density of the clump. The ratio of gravitational force to gas pressure gives a two-phase Jeans parameter, JtJ_tJt, which is the classical Jeans parameter with the sound speed replaced by an the wave speed in a coupled two-fluid medium. Its use makes the results insensitive to the initial density ratio of particles to gas as a separate parameter. An ordinary differential equation model is developed which takes the form of two coupled non-linear oscillators and reproduces key features of the simulations. Finally, a parametric study of the time to collapse is performed and a formula (fit to the simulations) is developed. In the incompressible limit Jtto0J_t \to 0Jtto0, collapse time equals sedimentation time. As JtJ_tJt increases, the collapse time decreases roughly linearly with JtJ_tJt until Jtgtrsim0.4J_t \gtrsim 0.4Jtgtrsim0.4 when it becomes approximately equal to the dynamical time.

Aps Division of Fluid Dynamics Meeting Abstracts, 2003

The persistence of condensation trails, "contrails", in the far-field of an aircraft wake is nume... more The persistence of condensation trails, "contrails", in the far-field of an aircraft wake is numerically analyzed. Contrails are ice clouds formed by condensation of exhaust water vapor in a cold atmosphere. Their evolution and persistence are controlled by the wake dynamics, atmospheric turbulence, as well as by background water vapor content. Under suitable atmospheric conditions, they may trigger the formation of cirrus clouds, thus having a potential climate impact on regional/global scales. The object of the present study is to reproduce the contrail evolution numerically in intermediate scales (between aircraft- and atmosphere- scales) where exhaust mixing and clouds microphysics are expected to control their dynamics and, eventually, their transition to cirrus clouds. The simulations are carried out using a two-phase approach to deal with both gas and ice phases. Large eddy simulations are used for the gas phase while a Lagrangian particles tracking approach is used for ice crystals. Mass transfer between the two phases is used to account for vapor condensation, by employing available ice microphysics models. Besides the physical description of the phenomenon, the results may be useful for "calibrating" source terms, representative of the environmental impact of aircraft-generated emissions, in global climate codes.

Aps Division of Fluid Dynamics Meeting Abstracts, Feb 1, 1997

Initial results from the direct numerical simulation (DNS) of compressible turbulent boundary lay... more Initial results from the direct numerical simulation (DNS) of compressible turbulent boundary layers will be presented. The spatially developing boundary layer is first transformed to a parallel shear layer using a transformation similar to that used by Spalart for an incompressible boundary layer. This allows us to avoid inflow and outflow boundary conditions, and to apply periodic boundary conditions in the streamwise and spanwise directions. The resulting equations are then solved using a mixed Fourier B-spline Galerkin method. One challenge to these highly accurate and non-dissipative numerics has been the occurrence of sharp density gradients, which require significantly more resolution than the incompressible case, especially during transients. The first simulation is at Mach 2.5 with a momentum thickness Reynolds number based on wall viscosity of R_θ'=825. The simulations are used to examine the physics of the compressible boundary layer and to compute turbulence statistics and terms in the budget equations. The turbulence statistics include: rms and mean profiles, energy spectra, and two-point correlations.

When analytes containing cationic components, such as proteins, are separated in fused silica cap... more When analytes containing cationic components, such as proteins, are separated in fused silica capillaries or micro-chips, they adsorb strongly to the negatively charged walls. Broadened and highly asymmetric peaks in the detector signal is symptomatic of the presence of such wall interactions. Band broadening is caused by a reduction in wall zeta potential at the adsorbed sites which in turn introduces a shear into the electroosmotic flow which leads to Taylor dispersion. In this work, numerical solutions of the coupled electro-hydrodynamic equations for fluid flow and the transport equation for analyte concentration were undertaken in the limit of thin Debye layers. The calculations reproduce many of the qualitative effects of wall adsorption familiar from observation. Further, the simulation results are compared, and found to agree very well with a recently developed asymptotic theory (Ghosal, S., (2003) J. Fluid Mech., 491, 285--300.)

ABSTRACT Several two-equation turbulence models are compared to data from direct numerical simula... more ABSTRACT Several two-equation turbulence models are compared to data from direct numerical simulations (DNS) of the homogeneous elliptic streamline flow, which combines rotation and strain. The models considered include standard two-equation models and models with corrections for rotational effects. Most of the rotational corrections modify the dissipation rate equation to account for the reduced dissipation rate in rotating turbulent flows, however, the DNS data shows that the production term in the turbulent kinetic energy equation is not modeled correctly by these models. Nonlinear relations for the Reynolds stresses are considered as a means of modifying the production term. Implications for the modeling of turbulent vortices will be discussed.

Journal of Computational Physics, May 1, 1999

A numerical technique for computations of turbulent flows is described. The technique is based on... more A numerical technique for computations of turbulent flows is described. The technique is based on B-splines and allows grid embedding in physically significant flow regions. Numerical tests, which include solutions of nonlinear advection-diffusion equations and computations of flow over a circular cylinder at Reynolds numbers up to 300, indicate that the method is accurate and efficient. In computations of flow over a cylinder, the lift, drag, and base suction coefficients agree well with existing experimental data and previous numerical simulations.

Direct numerical simulations are performed for homogeneous turbulence with a mean flow having ell... more Direct numerical simulations are performed for homogeneous turbulence with a mean flow having elliptic streamlines. This flow combines the effects of rotation and strain on the turbulence. Qualitative comparisons are made with linear theory for cases with high Rossby number. The nonlinear transfer process is monitored using a generalized skewness. In general, rotation turns off the nonlinear cascade; however, for moderate ellipticities and rotation rates the nonlinear cascade is turned off and then reestablished. Turbulence statistics of interest in turbulence modeling are calculated, including full Reynolds stress budgets.

Aps Division of Fluid Dynamics Meeting Abstracts, Nov 1, 1997

The formation of vortex rings generated through impulsively started jets is studied through using... more The formation of vortex rings generated through impulsively started jets is studied through using a piston/cylinder arrangement. For a wide range of piston stroke to diameter ratios (L/D), the DPIV results indicate that the flow field generated by large L/D consists of a leading vortex ring followed by a trailing jet. The vorticity field of the formed leading vortex ring is disconnected from that of the trailing jet. On the other hand, flow fields generated by small stroke ratios show only a single vortex ring. The transition between these two distinct states is observed to occur at a stroke ratio of approximately 4, which, in this paper, is referred to as the "formation number". This number indicates the maximum circulation attainable by a vortex ring. The universality of this number was tested by generating vortex rings with different jet exit boundaries, as well as with various non- impulsive piston velocities. The mere existence of the "formation number" is intriguing since it hints at the possibility that nature uses this time scale for some evolutionary incentives such as optimum ejection of blood from the left atrium to the heart's left ventricle or locomotion process where ejection of vortices might have been utilized for the purposes of propulsion.

Aiaa Journal, Apr 30, 2012